Problem: If 52 cards are dealt to 8 people as evenly as possible, how many people will end up with fewer than 7 cards?
Solution: When you divide 52 by 8, you get 6 with a remainder of 4.  Therefore, 4 of the people will get an extra card, bringing their total to 7, while the remaining $\boxed{4}$ people have only 6 cards.